Question

Which function describes this graph?

-61
-5
▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬
O A. y = (x+5)(x-3)
OB. y-(x-2)(x - 5)
OC. y = x² +5x+12
OD. y=x+7x+10
5

Answer 1

D. y = x² +7x +10

Explanation:

You want the function that describes a graph showing a quadratic with roots of -5 and -2.

Equation

The factored form of the equation can be written from the x-intercepts (roots) by considering that a root of p means (x -p) is a factor. The factored equation is ...

y = (x -(-5))(x -(-2)) = (x +5)(x +2) . . . . . doesn't match A or B

When this is multiplied out, it becomes ...

y = x² +5x +2x +10 = x² +7x +10 . . . . . . matches choice D

The equation is y = x² +7x +10.